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If each gridline is 1m as indicated in the figure below, and the force F = 900 N, which of the following is the magnitude of the moment of the said force about the point A, in Nm? Select the correct response: none of these or 4454.772 or 2545.584 or 1909.188 or 5939.697

To solve this problem, we need to calculate the moment (torque) of the force \( F = 900 \, \text{N} \) about point \( A \). The moment of a force about a point is given by the formula:

\[
M = F \times d
\]

where:
- \( F \) is the force applied (900 N in this case).
- \( d \) is the perpendicular distance from point \( A \) to the line of action of the force.

### Step-by-Step Analysis

1. **Identify Points A, B, and Force Line:**
   - Point \( A \) is at \((1, 1)\) on the grid.
   - Point \( B \) is at \((8, 5)\) on the grid.
   - The force vector \( F \) appears to act from a point on the line between two grid points towards point \( B \).

2. **Determine the Perpendicular Distance:**
   The perpendicular distance \( d \) from point \( A \) to the line of action of force \( F \) is the shortest distance from point \( A \) to the line extending between the force points. We can find this using the formula for the distance from a point to a line in 2D:

   The line passes through points \( (7, 5) \) and \( (8, 5) \) giving a slope, calculate using:

   \[
   d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
   \]

   After finding \( d \) plug in the values to compute:

Finally choose the option the closest to your result.


Learn how to calculate the moment of a 900 N force about point A using the perpendicular distance method. This problem involves physics concepts like torque and the formula M = F × d, suitable for high school students in Grades 10-12.

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